Brendan Rogers rescued the Icelandic international from the Hoffenheim substitute bench during the January transfer window.
The 22-year-old has failed to establish himself as a first team regular following his move to the Bundesliga in 2010.
Since returning to England, Sigurdsson has repaid Rogers' faith by scoring five goals in nine games for the Swans.
"I was on the bench for a long period of time and I just wanted to play football so they let me go out on loan," said Sigurdsson. "Things will become clearer in the summer.
"Brendan was a factor in me coming here, he didn't need to convince me. I told him straight away that I wanted to come and join."
Rogers and Sigurdsson have previously worked together at Reading.